We report on the generation of noise-like pulse (NLP) trains in a Tm-doped fiber laser mode-locked by multilayer graphene saturable absorber. The spectral bandwidth obtained directly from the oscillator exceeds 60 nm, centered at 1950 nm, with 23.5 MHz repetition rate. The pulses were also amplified in a fully fiberized amplifier based on a double-cladding Tm-doped fiber. The system was capable of delivering 1.21 W of average power, which corresponds to 51.5 nJ energy stored in the noise-like bundle. We believe that the presented source might serve as a pump for supercontinuum generation in highly nonlinear fibers.